You might feel you need a running narration to grasp how the choreography of ODC Dance's "Triangulating Euclid" connects with the father of geometry and a priceless edition of his work. Not to fret: The secret lies in the movement itself.

There's a point-to-point logic to the piece that seems as irresistible and inevitable as those ancient mathematical theorems. The new work, seen during Sunday's matinee at Yerba Buena Center for the Arts' Lam Research Theater, as part of the company's 42nd anniversary season, flows, twirls and regroups with utter confidence.

That's all the more astonishing when you consider that "Triangulating Euclid" is a three-way collaboration between independent choreographer Kate Weare, ODC Artistic Director Brenda Way and company Co-Artistic Director KT Nelson. Modern dance is not sausage making, and it might not be wise to decipher who is responsible for what here.

The three-part work begins with a voiceover; the conservator of the book (there's an exhibit in the YBCA lobby) muses, while Yayoi Kambara etches a flexing, spinning solo in a square of light, backed by Matthew Antaky's projection of what seems like a relief map. Kambara, like her nine company colleagues, is dressed in a black bathing suit. The other dancers arrive and seem, after fleeting if focused partnerships, to flow into unisons; a straight line of performers, in context, astonishes.

Soon, a dancer draws lines on the floor with a chalky substance, and the dancers clothe themselves in what resemble baggy shower curtains, surely the ugliest dance costumes of the season (I hope Way will reconsider these outfits when she revives the piece after this season). "Triangulating Euclid" succeeds in individual duets. The work draws technically assured, emotionally inflected renderings from the entire company, but the pleasure comes in small bursts.

The sound score, mostly unattributed, is something of a mess. The high point is two consecutive recordings of Schubert's song "Nacht und Traüme," accompanying breathtaking duets for Kambara and Dennis Adams and Maggie Stack and Corey Brady. More moments like this would have helped.

On Thursday, to conclude ODC Dance's season opening-night gala, Way introduced "Lifesaving Maneuvers," one of the choreographer's "message dances," and one of the more winning of the ilk. At the start, one notes the profusion of full-company promenades, as pairs travel in stiff unisons, the women's bodies tilted just so, and one senses a dystopian aura compatible with what one finds in Paul Taylor's darker works.

Those skewed bodies return throughout the piece. Generally, symmetries prevail here; a man and a woman will mount matching clumps of dancers, reach for each other and not quite connect. But order signifies something ominous in "Lifesaving Maneuvers"; maybe it's social conformity, perhaps it's the demise of the imagination.

What will save a life? You will find clues in Jay Cloidt's pastiche tape, which ranges from disparate bits like Michael Douglas' "Greed is good" speech to a remixed version of "Eleanor Rigby." The carillon passages are the most winning feature of the sound score, although the aroma of didacticism is thick in the air. Alexander V. Nichols' design of a curtain of illuminated strips is another of his winning visual schemes.

Bit by bit, disorder infiltrates the landscape. Bodies roll across the surface. And, at the end, Vanessa Thiessen and Justin Andrews sink to the center of the stage and comfort each other. Empathy brings salvation of a sort.

Back this season is "Transit: Next Stop," Nelson's hit pageant of urban life in motion and in repose. The choreographer observes fleeting and lasting relationships with insight and wit. Nico Muhly's bouncy score engages, Max Chen's bicycles (which get quite a workout) charm, the dancers are the sort you fall in love with. New this year are Barry Steele's appealing cityscape backdrops, striking enough to compete with the performers for your attention.

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